R: Eigenvalues of the companion coefficient matrix of a...
roots
R Documentation
Eigenvalues of the companion coefficient matrix of a VAR(p)-process
Description
Returns a vector of the eigenvalues of the companion coefficient matrix.
Usage
roots(x, modulus = TRUE)
Arguments
x
An object of class ‘varest’, generated by
VAR().
modulus
Logical, set to TRUE for returning the modulus.
Details
Any VAR(p)-process can be written in a first-order vector
autoregressive form: the companion form. A VAR(p)-process is stable,
if its reverse characteristic polynomial:
has no roots in or on the complex circle. This is equivalent to the
condition that all eigenvalues of the companion matrix A have
modulus less than 1. The function roots(), does compute the
eigen values of the companion matrix A and returns by default
their moduli.
Value
A vector object with the eigen values of the companion matrix, or
their moduli (default).
Author(s)
Bernhard Pfaff
References
Hamilton, J. (1994), Time Series Analysis, Princeton
University Press, Princeton.
Lütkepohl, H. (2006), New Introduction to Multiple Time Series
Analysis, Springer, New York.
See Also
VAR
Examples
data(Canada)
var.2c <- VAR(Canada, p = 2, type = "const")
roots(var.2c)